The present invention relates to an imaging assembly with a synthetic aperture optical instrument.
Using imaging optical systems with synthetic apertures is envisaged in the aerospace industry in particular. These systems consist in a combination of subsystems, each of small size, that achieves practically the same result as a large optical system. A system made up of small subsystems is easier to produce than a large optical system and causes less problems to launch by means of a satellite. An imaging system of this type has a telescope function, for example.
The signals obtained by each of the instruments are generally combined by Fizeau or Michelson interferometry.
FIG. 1 represents by way of illustration one pupil configuration of a three-telescope interferometer.
The main optical characteristic of a synthetic aperture optical device is determined by the diameter of the pupils 10, 12, 14 and their respective positions. In this example, the pupils all have the same diameter D′ and their centers are disposed in accordance with an equilateral triangle of side length B′.
It is known that synthetic aperture devices of this kind may have a modulation transfer function (MTF) whose support is discontinuous if the distance between the pupils is sufficiently large compared to their diameter, i.e. this function features cancellation ranges. FIG. 2 represents the modulation transfer function of the instrument represented in FIG. 1.
The modulation transfer function of an optical device is the response of the instrument to the diverse input spatial frequencies. In the FIG. 2 diagram, the column spatial frequencies are represented on the abscissa axis u and the row frequencies are represented on the ordinate axis v. The support of the modulation transfer function of the instrument represented in FIG. 1 therefore features seven circular regions, each having a diameter 2D (where D=D′/λ, λ being the wavelength): a “central” region LL for low column and line frequencies (L), and six peripheral circular regions: LH, HH, H′H, L′H, H′H′ and HH′. The notation LH means that the region relates to low row frequencies (L) and high column frequencies (H). Similarly, the notation HH, H′H, H′H′ and HH′ signifies high row and column frequencies.
The centers of the peripheral circular regions are on a circle of diameter 2B (where B=B′/λ) centerd on the origin.
The line joining the centers of the circles HH and H′H′ is at an angle of 60° to the abscissa axis and, similarly, the line joining the centers of the circles H′H and HH′ is at an angle of 120° to the abscissa axis.
In practice, the images are sampled with a spatial sampling frequency that may be different for the rows and the columns. To prevent aliasing, i.e. loss of information, it is necessary to comply with Shannon's theorem, i.e. the column sampling frequency must be greater than or equal to twice the maximum frequency of the spectrum to be reproduced, i.e. twice the distance I (FIG. 2) such that I=B+D, and, the row sampling frequency must be equal to twice the distance μ (FIG. 2), where μ=√3B/2+D.
Accordingly, when the column sampling frequency is 2B+2D and the row sampling frequency is √3B/2+D, an image is obtained for which the support of the spectrum is of the type represented in FIG. 3 with a central spectrum section comprising the seven circular regions LL, L′H, LH, HH, H′H′, H′H and HH′ and delimited in FIG. 3 by a rectangle 200,0. The spectrum also comprises a set of replicas identical to the central section offset on the abscissa axis by an integer number of column sampling frequencies and on the ordinate axis by an integer number of row sampling frequencies.
Accordingly, as may be seen in FIG. 3, the central rectangle 200,0 of the usable portion of the spectrum is replicated to form paving with slabs identical to the central slab 200,0 constituting replicas 201,0, 200,1, 201,1, 200,−1, 20−1,1, etc.
Until now, it has been considered that the sampling frequency could not fall below values corresponding to those of FIG. 3 since, for lower sampling frequencies, the MTF regions of the replicas overlap the MTF regions of the central section 200,0, which would lead to aliasing, i.e. to degrading of the information.
The number of pixels (picture elements) necessary for sampling the image is, of course, a direct function of the sampling frequency. As a result of this, the higher the sampling frequency, the higher the number of pixels that is necessary.